Electrical transformer

ABSTRACT

The present invention relates to an electrical transformer which includes a primary winding coupled to first and second magnetic circuits. A magnetic flux is driven through the magnetic circuits by the primary winding. First and second secondary windings are also provided, each associated with a respective one of the magnetic circuits and being electrically connected together in series opposition. A closed superconducting fault current winding is also provided to link with the magnetic flux in the second magnetic circuit.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional of application Ser. No. 09/379,607,filed Aug. 24, 1999, now U.S. Pat. No. 6,300,856.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to electrical transformers, for example for use inthe power distribution industry.

2. Description of the Prior Art

Electrical transformers are used in a variety of applications to stepdown (or step up) a voltage supply to a load. When large voltages areinvolved, problems can arise when a fault develops in the load resultingin a sudden demand for power. Typically, this is dealt with by includingcircuit breakers and the like but these are expensive and not alwaysreliable.

SUMMARY OF THE INVENTION

In accordance with the present invention, an electrical transformercomprises a primary winding; first and second magnetic circuitsmagnetically coupled with the primary winding and through which magneticflux is driven by the primary winding; first and second secondarywindings each associated with a respective one of the magnetic circuitsand electrically connected together in series opposition; and ashort-circuited superconducting winding, hereinafter known as the “faultcurrent winding” linked by the magnetic flux in the second magneticcircuit.

We have developed a transformer which incorporates automatic faultcurrent limiting by making use of a closed or short circuitedsuperconducting winding. In use, the secondary windings will beconnected to a load and under normal conditions, when the load impedanceis high enough not to draw excessive current, the superconducting faultcurrent winding has current induced in it which opposes the magneticflux linkage in the second magnetic circuit. The second secondarywinding therefore has no electromotive force induced in it, and theoutput of the transformer is determined by the properties of the primarywinding and the first secondary winding only.

In the event of a fault, such as a reduction in load impedance, or ashort circuit in the output circuit, the current in the fault currentwinding will rise. When it exceeds the superconducting critical current,the shorted winding becomes resistive, and if the resistance is greatenough, the induced electromotive force is not sufficient to drive acurrent through the fault current winding which opposes all the fluxlinkage. This allows an electromotive force to be induced in the secondsecondary winding, which opposes that of the first secondary winding.This effect therefore reduces the output voltage of the transformer soas to limit the current which can be drawn from it.

The use of a superconducting fault current winding to achievefault-current limitation is desirable because the mechanism isfail-safe, very fast, has no moving parts and is self-sensing. Also, atlarger ratings, this approach becomes much more commercially viable incomparison with conventional circuit breakers.

Although the transformer could be constructed from resistive windings,preferably the primary and secondary windings are superconductive.

In the case of transformers, there is a potential saving in eliminatingthe ohmic loss in the windings, provided that the refrigeration cost canbe made small enough. Also, superconducting transformers could be morecompact because of the higher current density in the windings and theelimination of coolant circulation and heat-exchange hardware.

By making all the windings superconducting, the transformer principleallows properties of the superconductor to be matched to the applicationso that the superconducting material can be used in a form which can bereadily manufactured and is robust.

Most conveniently, the primary, secondary and fault current windings arehoused in a common cryostat. This significantly reduces therefrigeration overhead compared with independent systems.

It is possible to utilize a single turn for the fault current windingalthough a coil having more than one turn could also be used.

Typically, the reluctances of the two magnetic circuits will be similar,so that the current in the fault current winding is proportional to thecurrent in the primary winding, which is in turn determined by the loadimpedance.

The transformer can be conveniently designed with identicalcross-sections and lengths of iron (or other magnetic material such asferrite) in the two magnetic circuits. However, under normal conditions,the first (not coupled to the fault current winding) will carry moreflux than the second, so that the iron will be operating over adifferent part of its B/H curve, so that the reluctance will be slightlydifferent. So long as the iron is not saturated, this difference shouldnot affect the operation of the device.

BRIEF DESCRIPTION OF THE DRAWINGS

An example of an electrical transformer according to the invention willnow be described with reference to the accompanying drawings, in which:

FIG. 1 is a circuit diagram of the transformer connected to a supply anda load; and

FIG. 2 is a schematic circuit diagram used for performing the SPICEmodel to be described.

DETAILED DESCRIPTION OF THE EMBODIMENT

The transformer shown in FIG. 1 comprises a pair of rectangular, ironyokes 1,2 defining respective first and second magnetic circuits andlying alongside one another. Adjacent arms 1A,2A of the magneticcircuits 1,2 pass through a primary winding 3 of the transformer whichis connected to a supply 4.

First and second secondary windings 5,6 are provided around the magneticcircuits 1,2 respectively and are connected in series opposition to eachother and to a load 7.

As mentioned above, although the windings 3,5,6 could be resistive,preferably they are superconductive and will be mounted in a suitablecryostat. A shorted turn 8 of superconductor is provided around an armof the magnetic circuit 2.

As described above, under normal conditions, when the load impedance ishigh enough not to draw excessive current, the shorted turn 8 has acurrent induced in it which opposes the magnetic flux linkage in themagnetic circuit 2. The second secondary winding 6 therefore has noelectromotive force induced in it and the output of the transformer isdetermined by the properties of the primary winding 3 and the firstsecondary winding 5.

When a fault such as a reduction in load impedance occurs, the currentin the shorted turn 8 will rise. When it exceeds the superconductingcritical current, the shorted turn 8 will become resistive, and if theresistance is great enough, the induced electromotive force is notsufficient to drive a current through the turn 8 which opposes all theflux linkage. This allows an electromotive force to be induced in thesecond secondary winding 6 which opposes that of the first secondarywinding 5. This effect then reduces the output voltage of thetransformer so as to limit the current which can be drawn from it.

The following summarizes a mathematical analysis of the system which hasbeen carried out using the DERIVE program published by Soft WarehouseInc., of Honolulu, Hawaii, USA.

The circuit equations for a system of inductively coupled circuits canbe described by the vector equation:

{overscore (V)}=(jω{overscore (M)}+{overscore (R)}).{overscore (I)}  (1)

where

M is the mutual inductance matrix, and

R is a diagonal matrix containing the resistances of each circuit.

In the circuit shown in FIG. 1: $\begin{matrix}{V = \left\lbrack {V_{supply},0,0} \right\rbrack} \\{I = \left\lbrack {I_{prim},I_{\sec},I_{short}} \right\rbrack} \\{M = {\begin{matrix}L_{p} & {M_{p,{s1}} - M_{p,{s2}}} & M_{p,{s3}} \\{M_{p,{s1}} - M_{p,{s2}}} & {L_{s1} + L_{s2}} & M_{{s2},{s3}} \\M_{p,{s3}} & M_{{s2},{s3}} & L_{s3}\end{matrix}}} \\{R = {\begin{matrix}R_{supply} & 0 & 0 \\0 & R_{load} & 0 \\0 & 0 & R_{short}\end{matrix}}}\end{matrix}$

Where the subscripts have the following meanings:

p,prim refer to the primary coil,

sec refers to the series current in the secondary coils,

s1 refers to the secondary winding 5,

s2 refers to the secondary winding 6,

s3 refers to the shorted, superconducting coil 8,

L is inductance, and

M is mutual inductance.

Note that there is no coupling between winding 5 and winding 6, orbetween winding 5 and turn 8, because they are on difference magneticcircuits.

The inductances can be described in terms of the number of turns, n_(p),n_(s) (n_(s) is the number of turns in one of the secondary windings,5,6, the secondary windings 5 and 6 having equal turns in this analysis)and the core dimensions given by:$K = {\mu \quad \mu_{0}\frac{A}{I}}$

where:

A is the cross-sectional area of the magnetic circuit, and

I is the length of the flux path around the magnetic circuit.

M_(p,s1)=n_(p) n_(s) k K etc

where leakage is allowed for in the coupling constant k,

L_(p)=n_(p) ² k 2K

L_(s1)=n_(s1) ² K etc.

It is also convenient to work in terms of${{Turns}\quad {ratio}\quad a} = \frac{n_{p}}{n_{s}}$${{Second}\quad {turns}\quad {ratio}\quad a_{2}} = \frac{n_{s}}{n_{3}}$

where:

n₃ is the number of turns in the shorted turn 8.

Ratio of actual to nominal load impedance$\delta = \frac{R_{load}}{{nominal}\text{-}{load}}$

Ratio of secondary coil impedance to nominal load$\beta = \frac{\omega \left( {L_{{s1}\quad} + L_{s2}} \right)}{{nominal}\text{-}{load}}$

Equation 1 can then be solved for the currents in each circuit. Theexpressions which are obtained are extremely large, but capable of beingused. In order to present the results in a more comprehensible form,some simplifying assumptions may be made.

The supply has a negligible output impedance,

R_(supply)=0;

There is no flux leakage,

k=1.

The results can then be tabulated (Table 1) for the two conditions:

“Normal”−R_(short)=0 (superconductive)

“Fault”−R_(load)=0, R_(short) non-zero (resistive).

TABLE 1 Normal Fault I_(prim)$\sqrt{1 + {4\quad \frac{\delta^{2}}{\beta^{2}}}}\frac{V_{supply}}{\alpha^{2\quad}\delta \quad {nominal\_ load}}$

$\begin{matrix}\sqrt{1 + \left( \frac{4\alpha_{2}R_{short}}{\beta \quad {nominal\_ load}} \right)^{2}} \\\frac{V_{supply}}{\alpha^{2}\alpha_{2}^{2}R_{short}}\end{matrix}$

I_(sec)$\frac{V_{supply}}{\alpha \quad \delta \quad {nominal\_ load}}$

$\frac{V_{supply}}{4{\alpha\alpha}_{2}^{2}R_{short}}$

I_(short)$2\sqrt{1 + \left( \frac{\delta}{\beta} \right)^{2}}\frac{\alpha_{2}V_{supply}}{\alpha \quad \delta \quad {nominal\_ load}}$

$\frac{V_{supply}}{2{\alpha\alpha}_{2}R_{short}}$

It is also possible to model this system using SPICE. SPICE is a wellknown program for modeling electronic circuits, originally developed bythe University of California at Berkeley, and available in a number ofimplementations. This enables the non-linearity of the magnetic circuitsto be included, and the validity of the simplifications mentioned aboveto be investigated. However, the SPICE algorithm imposes somelimitations, and in particular does not allow a circuit to contain zeroresistance. In the following, the superconductor was modeled by aresistance of 10⁻⁶ ohm and the short circuit by 0.001 ohm.

The following values were used in the above analytical expressions andalso in a SPICE model, whose circuit schematic is shown in FIG. 2.

In this model, it is assumed that:

A =  0.047 m² I =   0.72 m n₃ = 1 n_(s) = 18 n_(p) = 1800 V_(supply) =20 kV nominal load =   4 ohms

For the expressions μ=1802, and in the SPICE model the following BHcurve was used:

B H tesla A/m 0.00 0.0 0.60 191 1.20 530 1.43 889 1.51 1206 1.57 16941.63 2414 1.73 4283 1.80 6012 1.85 7772 1.90 9788 1.95 12229 2.00 149892.08 20010 2.20 27806

The results of these two calculations are compared in Table 2 below fordifferent values of R_(short).

TABLE 2 R_(short) Normal Fault ohms Expressions SPICE Expressions SPICEI_(prim) 0.001 0.517 0.509 6.173 1.543 0.01 0.686 0.161 0.1 0.065 0.050I_(sec) 0.001 50.00 49.98 154.3 154.3 0.01 17.15 15.40 0.1 1.591 1.540I_(short) 0.001 1816 1806 5556 5551 0.01 617.3 555.0 0.1 57.27 55.8

Agreement is good, except at very low values of R_(short).

In the example which has been used, good limiting has been obtained fora normal-state resistance of 0.01 ohms. For the given core size, aresistivity of 10⁻⁶ ohm-metres and a critical current of 2000 A, thisrequires a critical current density of 2.5 10⁷ A/m², which is relativelyundemanding.

The above example has used equal numbers of turns on the two secondarywindings 5,6. However it is possible to use different numbers of turns,and thereby accommodate the properties of the superconductor (therelationship between critical current and resistance) to therequirements of the current limiter.

Table 3 below plots the fault currents against R_(short) for differentnumbers of turns on the second secondary winding.

TABLE 3 R_(short) ohms 9 turns 18 turns 36 turns I_(prim) 0.001 2.741.54 0.688 0.005 0.551 0.388 0.147 0.01 0.280 0.161 0.087 0.05 0.0770.057 0.055 0.1 0.060 0.051 0.054 I_(sec) 0.001 274 154 68.76 0.005 54.930.9 13.8 0.01 27.5 15.4 6.94 0.05 5.9 3.08 1.74 0.1 3.5 1.54 1.27I_(short) 0.001 7397 5551 3702 0.005 1481 1111 741 0.01 741 555 370 0.05148 111 74.1 0.1 74.1 55.6 37.0

If, for example, we wished to limit the secondary current to 15 A underfault conditions, this could be achieved with the following values ofR_(short), for different numbers of turns (Table 4). The correspondingvalue of the rated current in the shorted turn, under normal conditions,is also shown. Choosing the critical current to be 25% greater thanthis, the critical current density (J_(c)) of the superconductor 8 canthen be calculated.

TABLE 4 9 turns 18 turns 36 turns R_(short) for fault I_(sec) = 15 A, Ω0.02 0.01 0.0045 I_(short), rated normal, A 1361 1806 2704Superconductor section mm² 41.5 83 184 Power for fault kW 2.74 3.09 3.05Power density kW/m³ 79600 45000 19900 Current density (J_(c)) Amm⁻² 4127 18

In this analysis, we have assumed that the superconducting shorted turn8 is a cylinder. The inner radius is fixed by the size of the magneticcore plus an allowance for insulation etc. (the core diameter is in turndetermined by the power rating of the transformer). We also assume thatthe resistivity of the, superconductor has a value of 10⁻⁶ ohm-metre. Agiven resistance around this turn then defines the cross-sectional arearequired.

What is claimed is:
 1. A method of controlling fault current in atransformer, comprising: inducing current in a first winding through afirst magnetic circuit magnetically coupled to a primary winding; andinducing current in a second winding, in series opposition to thecurrent generated in the first winding, through a second magneticcircuit magnetically coupled to the primary winding, where the secondmagnetic circuit includes a closed circuit fault current winding,wherein the current in the second winding is increased, when currentinduced in the fault current winding exceeds a critical current.
 2. Themethod of controlling fault current of claim 1, further comprising:generating an output current based on the current in the first andsecond windings and the fault current winding.
 3. The method ofcontrolling fault current of claim 1, wherein the fault current windingis a superconductor.